An Exposition of Iwasawa Theory
Specialeforsvar ved Péter Zarándy
Title: An Exposition of Iwasawa Theory
Abstract: In this thesis we give an exposition of selected topics in Iwasawa theory. By introducing the Iwasawa module and providing an in-depth ring and module theoretic description of the ring ℤ𝑝 [[𝑇 ]], we give a proof of Iwasawa’s theorem on the asymptotic behaviour of the 𝑝-part of the class numbers in a ℤ𝑝 -extension. Then, after giving Iwasawa’s construction of 𝑝-adic 𝐿-functions and a generalization of Iwasawa modules with an action of the Galois group on it, we state the Main Conjecture of Iwasawa theory for imaginary abelian number fields and give a high level description of a modern proof using the Euler systems of Gauss sums.
Vejleder: Ian Kiming
Censor: Pieter Hendrik Turdus Beelen, DTU